Compact Extra Dimensions Research Articles

Does the cosmological constant really indicate the existence of a dark dimension?

According to the “dark dimension” (DD) scenario, we might live in a universe with a single compact extra dimension, whose mesoscopic size is dictated by the measured value of the cosmological constant. This scenario is based on swampland conjectures that lead to the relation [Formula: see text] between the vacuum energy [Formula: see text] and the size of the extra dimension [Formula: see text] ([Formula: see text] is the mass scale of a Kaluza–Klein tower), and on the corresponding result [Formula: see text] from the effective field theory (EFT) limit. We show that [Formula: see text] contains previously missed UV-sensitive terms, whose presence invalidates the widely spread belief (based on existing literature) that the calculation gives automatically the finite result [Formula: see text] (with no need for fine-tuning). This renders the matching between [Formula: see text] and [Formula: see text] a nontrivial issue. We then comment on the necessity to find a mechanism that implements the suppression of the aforementioned UV-sensitive terms. This should finally allow to frame the DD scenario in a self-consistent framework, also in view of its several phenomenological applications based on EFT calculations.

Quantum [formula omitted]-Yang-Mills from the IKKT matrix model

We study the one-loop effective action of the higher-spin gauge theory induced by the IKKT matrix model on a M1,3×K background, where M1,3 is an FLRW cosmological spacetime brane and K are compact fuzzy extra dimensions. In particular, we show that all non-abelian (hs-valued) gauge fields in this model acquire mass via quantum effects, thus avoiding no-go theorems. This leads to a massive non-abelian quantum hs-Yang-Mills theory, whose detailed structure depends on K. The stabilization of K at one loop is understood as a result of the coupling between K and the U(1)-flux bundle on space-time. This flux stabilization induces the KK scale into the N=4 SYM sector of the model, which break superconformal symmetry.

Cosmological perturbations from five-dimensional inflation

It was recently proposed that five-dimensional inflation can relate the causal size of the observable universe to the present weakness of gravitational interactions by blowing up an extra compact dimension from the microscopic fundamental length of gravity to a large size in the micron range, as required in the Dark Dimension proposal. Here, we compute the power spectrum of all primordial fluctuations emerging from a 5-dimensional inflaton in a slow-roll region of its potential, showing an interesting change of behaviour at large scales corresponding to angles larger than about 10 degrees in the sky.

Large extra dimensions from higher-dimensional inflation

We propose the possibility that compact extra dimensions can obtain large size by higher-dimensional inflation, relating the weakness of the actual gravitational force to the size of the observable Universe. Solution to the horizon problem implies that the fundamental scale of gravity is smaller than 1013 GeV, which can be realized in a braneworld framework for any number of extra dimensions. However, requirement of an (approximate) flat power spectrum of primordial density fluctuations consistent with present observations makes this simple proposal possible only for one extra dimension at around the micron scale. After the end of five-dimensional inflation, the radion modulus can be stabilized at a vacuum with positive energy of the order of the present dark energy scale. An attractive possibility is based on the contribution to the Casimir energy of right-handed neutrinos with a mass at a similar scale. Published by the American Physical Society 2024

Neutralizing topological obstructions to bubbles of nothing

Theories with compact extra dimensions can exhibit a vacuum instability known as a bubble of nothing. These decay modes can be obstructed if the internal manifold is stabilized by fluxes, or if it carries Wilson lines for background gauge fields, or if the instanton is incompatible with the spin structure. In each of these cases the decay can proceed by adding dynamical charged membranes or gauge fields. We give a general, bottom-up procedure for constructing approximate bubble of nothing solutions in models with internal spheres stabilized by flux and study the influence of the brane tension on the tunneling exponent, finding two branches of solutions that merge at a minimal superextremal value of the tension. In the case of Wilson operators and incompatible fermions, the relevant bubble is shown to be the Euclidean Reissner-Nordstrom black hole, and the ordinary decay exponent is modified by 1/g2 effects. We examine the Dirac operator on this background and comment on the relevance for models of supergravity with gauged R-symmetry.

Photon region and shadow of a rotating 5D black string

To explore the possible clues for the extra dimension from the Event Horizon Telescope (EHT) observations, we study the shadow of the rotating 5D black string in General Relativity (GR). Instead of investigating the shadow in the effective 4D theory, we concern the motion of photons along the extra dimension z with a conserved momentum P_z, which appears as an effective mass in the geodesic equations of photons. The existence of P_z enlarges the photon regions and the shadow of the rotating 5D black string while it has slight impact on the distortion. The EHT observations of M87* and SgrA* can rule out the black string model with an infinite length along the extra dimension, and support the hypothesis that the extra dimension is compact to avoid the Gregory-Laflamme (GL) instability, where the length of the black string/the compact extra dimension can be constrained as 2.03125~textrm{mm} lesssim ell lesssim 2.6~textrm{mm} and 2.28070~textrm{mm} lesssim ell lesssim 2.6~textrm{mm} respectively.

On aether terms in a space-time with a compact extra dimension

In this paper, we explicitly calculate the aether-like corrections for the electromagnetic field in the case when the space-time involves an extra compact spatial dimension besides of usual four dimensions. Our methodology is based on an explicit summation over the Kaluza–Klein tower of fields which turns out to be no more difficult than the finite-temperature calculations. We found some new terms which can be treated as certain five-dimensional generalizations of the aether-like terms kappa ^{mnpq}F_{mn}F_{pq} and bar{psi }c^{mn}gamma _mpartial _n psi which in four dimensions are treated as important ingredients of the Lorentz-breaking extension of the standard model. We have shown that these new terms become to dominate in the limit where the extra dimension is very small, allowing us to suggest that there will be essential modifications of quantum corrections if our space indeed has a small extra spatial dimension. Moreover, we have shown that in the CPT-even case we have extra new particles as a consequence of the extra dimension.

Five-dimensional Einstein–Gauss–Bonnet gravity compactified and applied to a colour-flavour-locked equation of state

Einstein–Gauss–Bonnet gravity in five dimensions is applied to compact stellar objects, in particular to quark stars obeying a colour-flavour-locked equation of state. Matter under such extreme conditions welcomes the use of higher-order gravity theories or the inclusion of extra dimensions in support of higher-curvature effects. In so doing, we focus on the representation of quantities in higher dimensions in standard four-dimensional spacetime via compactification. Invoking extra compact dimensions from a basic string-theoretic perspective provides for the rationalisation of physical quantities computed in higher dimensions.

One-loop effective action and emergent gravity on quantum spaces in the IKKT matrix model

A detailed derivation of 3 + 1 dimensional induced or emergent gravity in the IKKT matrix model at one loop is given, as announced in [1]. The mechanism requires a brane configuration with structure {mathcal{M}}^{3,1}times mathcal{K}subset {mathbb{R}}^{9,1} , where {mathcal{M}}^{3,1} is the noncommutative space-time brane, and mathcal{K} are compact fuzzy extra dimensions embedded in target space. The 3+1-dimensional Einstein-Hilbert action then arises in the one loop effective action of the maximally supersymmetric IIB or IKKT matrix model, with effective Newton constant determined by the Kaluza-Klein scale of mathcal{K} . At weak coupling, all physical modes are confined to the brane, leading to 3 + 1-dimensional low-energy physics. The Einstein-Hilbert action can be interpreted as interaction of mathcal{K} with the space-time brane via IIB supergravity. The vacuum energy does not act as cosmological constant, but stabilizes the brane structure at one loop.

Superluminal anisotropic propagation and wavefront splitting on tilted and boosted braneworlds

Braneworlds winding and spinning around an extra compact dimension manifest superluminal propagation for fields penetrating the bulk. This propagation is either irreducibly anisotropic or one that becomes isotropic in a special frame, depending on the brane's motion and orientation in the bulk. For a class of boosted observers on the brane the wavefront of such fields will split into two components, one propagating forward and the other backward in time at superluminal speeds. In spite of these effects, there is no violation of causality and no tachyons. Detection of astrophysical anisotropic superluminal propagation velocities would offer a sign for the existence of extra compactified dimensions.

Distortion of extra dimensions in the inflationary multiverse

The observable inflation is a final step in a slow evolution of our space. The latter occurs starting from the Planck scale, so that eventually a huge number of causally disconnected regions of space (pocket universes) will appear. The Multiverse thus formed consists of similar universes and, therefore, does not fulfill its mission. Here, we discuss the way to improve the situation. We study the effect of the quantum fluctuations at high energies on the shape of compact extra dimensions which turn out to be specific to each pocket universe. Low-energy physical parameters depend on extra dimensional metric. Therefore, the low-energy physics is different in different pocket universes. The numerical estimation of the probability of finding a particular metric is based on the model of compact two-dimensional extra space.

Casimir effect in DFR space–time

Noncommutative space–time introduces a fundamental length scale suggested by approaches to quantum gravity. Here, we report the analysis of the Casimir effect for parallel plates separated by a distance of [Formula: see text] using a Lorentz invariant scalar theory in a noncommutative space–time (DFR space–time), both at zero and finite temperatures. This is done in two ways; one when the additional space-dimensions introduced in DFR space–time are treated as extra dimensions but on par with usual space-dimension and in the second way, the additional dimensions are treated as compact dimensions. Casimir force obtained in the first approach coincides with the result in the extra-dimensional commutative space–time and this is varying as [Formula: see text]. In the second approach, we derive the corrections to the Casimir force, which is dependent on the separation between the plate, [Formula: see text] and on the size of the extra compactified dimension, [Formula: see text]. Since correction terms are very small, keeping only the most significant terms of these corrections, we show that for certain values of the [Formula: see text], the corrections due to noncommutativity make the force between the parallel plates more attractive, and using this, we find lower bound on the value of [Formula: see text]. We show here that the requirement of the Casimir force and the energy to be real impose the condition that the weight function used in defining the DFR action has to be a constant. At zero temperature, we find correction terms due to noncommutativity depend on [Formula: see text]- and [Formula: see text]-dependent modified Bessel functions [Formula: see text] and [Formula: see text], with coefficients that vary as [Formula: see text] and [Formula: see text], respectively. For finite temperature, the Casimir force has correction terms that scale as [Formula: see text] and [Formula: see text] in high-temperature limit and as [Formula: see text] and [Formula: see text] in the low-temperature limit.

The length of a compact extra dimension from black hole shadow

The length of a compact extra dimension from black hole shadow

Early dark energy from a higher-dimensional gauge theory

The Hubble constant estimated from the CMB measurements shows large disagreement with the locally measured value. This inconsistency is called the Hubble tension and is vastly studied in recent years. Early Dark Energy (EDE) gives a few percent contribution to the total energy density of the universe only at an epoch before the recombination, and it is considered as a promising solution to the tension. A simple realization of EDE is given by dynamics of a scalar field, called the EDE scalar, and models including the EDE scalar are extensively studied in the literature. In this paper, we present a novel EDE scenario based on higher-dimensional gauge theories. An extra component of gauge fields associated with a compact extra dimension behaves as the EDE scalar at low-energy and has a periodic potential, which has a similar form as potentials for pseudo Nambu-Goldstone bosons (PNGB). In a five-dimensional U(1) gauge theory, we show that a scalar field that originates from the gauge field can give EDE through its dynamics in a PNGB type potential with a suitable choice of parameters in the theory. We focus on the scenario where EDE is explained by the scalar field and clarify constraints on the fundamental parameters of the gauge theory, such as the gauge coupling, the compactification scale, and the mass parameters for matter fields. We also find that a sufficient dilution of EDE requires non-trivial relations among U(1) charges of matter fields. With specific matter contents, we numerically solve the time evolution of the scalar field and confirm that its energy density behaves as an EDE. In our scenario, the parameters of the gauge theory and predicted properties of EDE are related to each other. Thus, the cosmological restrictions on the EDE properties provide insights into higher-dimensional gauge theories.

Compact extra dimensions as the source of primordial black holes

This article discusses a model of primordial black hole (PBH) formation at the reheating stage. These small/massive black holes appear due to the specific properties of the compact extra dimensions. The latter gives rise to the low energy model, containing an effective scalar field potential capable of domain wall production. Formed during inflation, these walls are quite dense, meaning they collapse soon after inflation ends. Discussion of the model is framed by the scope of multidimensional f(R)-gravity. We study the possibility of the pure gravitational formation of primordial black holes (PBHs). Interpreting the scalar curvature of compact extra space Rn as an effective scalar field in an Einstein framework and consider effective scalar-field theory that might potentially be capable of producing domain walls with a certain choice of parameters. Hence, we demonstrate that f(R)-gravity contains a mechanism for PBH formation. The study assumed that cosmological inflation is an external process, which satisfied all the cosmological constraints on our mechanism.

Primordial black hole dark matter in the context of extra dimensions

Theories of large extra dimensions (LEDs) such as the Arkani-Hamed, Dimopoulos & Dvali scenario predict a "true" Planck scale $M_\star$ near the TeV scale, while the observed $M_{pl}$ is due to the geometric effect of compact extra dimensions. These theories allow for the creation of primordial black holes (PBHs) in the early Universe, from the collisional formation and subsequent accretion of black holes in the high-temperature plasma, leading to a novel cold dark matter (sub)component. Because of their existence in a higher-dimensional space, the usual relationship between mass, radius and temperature is modified, leading to distinct behaviour with respect to their 4-dimensional counterparts. Here, we derive the cosmological creation and evolution of such PBH candidates, including the greybody factors describing their evaporation, and obtain limits on LED PBHs from direct observation of evaporation products, effects on big bang nucleosynthesis, and the cosmic microwave background angular power spectrum. Our limits cover scenarios of 2 to 6 extra dimensions, and PBH masses ranging from 10 to $10^{21}$ g. We find that for two extra dimensions, LED PBHs represent a viable dark matter candidate with a range of possible black hole masses between $10^{17}$ and $10^{23}$ g depending on the Planck scale and reheating temperature. For $M_\star = 10$ TeV, this corresponds to PBH dark matter with a mass of $M \simeq 10^{21}$ g, unconstrained by current observations. We further refine and update constraints on "ordinary" four-dimension black holes.

Hawking radiation of scalar particles and fermions from squashed Kaluza–Klein black holes based on a generalized uncertainty principle

We study the Hawking radiation from the five-dimensional charged static squashed Kaluza–Klein black hole by the tunneling of charged scalar particles and charged fermions. In contrast to the previous studies of Hawking radiation from squashed Kaluza–Klein black holes, we consider the phenomenological quantum gravity effects predicted by the generalized uncertainty principle with the minimal measurable length. We derive corrections of the Hawking temperature to general relativity, which are related to the energy of the emitted particle, the size of the compact extra dimension, the charge of the black hole and the existence of the minimal length in the squashed Kaluza–Klein geometry. We obtain some known Hawking temperatures in five and four-dimensional black hole spacetimes by taking limits in the modified temperature. We show that the generalized uncertainty principle may slow down the increase of the Hawking temperature due to the radiation, which may lead to the thermodynamic stable remnant of the order of the Planck mass after the evaporation of the squashed Kaluza–Klein black hole. We also find that the sparsity of the Hawking radiation modified by the generalized uncertainty principle may become infinite when the mass of the squashed Kaluza–Klein black hole approaches its remnant mass.

Gravity as a quantum effect on quantum space-time

The 3+1-dimensional Einstein-Hilbert action is obtained from the 1-loop effective action on noncommutative branes in the IIB or IKKT matrix model. The presence of compact fuzzy extra dimensions K as well as maximal supersymmetry of the model is essential. The E-H action can be interpreted as interaction of K with the space-time brane via IIB supergravity, and the effective Newton constant is determined by the Kaluza-Klein scale of K. The classical matrix model defines a pre-gravity action with 2 derivatives less than the induced E-H action, governing the cosmological regime. The perturbative physics is confined to the space-time brane, which for covariant quantum space-times includes all dof of gravity, as well as a tower of higher-spin modes. The vacuum energy of the background is given in terms of the symplectic volume form, and hence does not act as cosmological constant.

Gravitational memory and compact extra dimensions

We develop a general formalism for treating radiative degrees of freedom near ${\mathcal{I}}^{+}$ in theories with an arbitrary Ricci-flat internal space. These radiative modes are encoded in a generalized news tensor which decomposes into gravitational, electromagnetic, and scalar components. We find a preferred gauge which simplifies the asymptotic analysis of the full nonlinear Einstein equations and makes the asymptotic symmetry group transparent. This asymptotic symmetry group extends the Bondi--Metzner--Sachs (BMS) group to include angle-dependent isometries of the internal space. We apply this formalism to study memory effects, which are expected to be observed in future experiments, that arise from bursts of higher-dimensional gravitational radiation. We outline how measurements made by gravitational wave observatories might probe properties of the compact extra dimensions.

Casimir effect with one large extra dimension

In this work, I study the Casimir effect of a massive complex scalar field in the presence of one large compactified extra dimension. I investigate the case of a scalar field confined between two parallel plates in the macroscopic three dimensions, and examine the cases of Dirichlet and mixed (Dirichlet–Neumann) boundary conditions on the plates. The case of Neumann boundary conditions is uninteresting, since it yields the same result as the case of Dirichlet boundary conditions. The scalar field also permeates a fourth compactified dimension of a size that could be comparable to the distance between the plates. This investigation is carried out using the [Formula: see text]-function regularization technique that allows me to obtain exact expressions for the Casimir energy and pressure. I discover that when the compactified length of the extra dimension is similar to the plate distance, or slightly larger, the Casimir energy and pressure become significantly different than their standard three-dimensional values, for either Dirichlet or mixed boundary conditions. Therefore, the Casimir effect of a quantum field that permeates a compactified fourth dimension could be used as an effective tool to explore the existence of large compactified extra dimensions.